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Zbl 0811.17014
Van Daele, A.; Van Keer, S.
(Daele, A. van; Keer, S. van)
The Yang-Baxter and pentagon equation. (English)
[J] Compos. Math. 91, No.2, 201-221 (1994). ISSN 0010-437X; ISSN 1570-5846/e

For a finite-dimensional *-Hopf algebra $\cal A$ different embeddings of the quantum double ${\cal D}({\cal A})$ into its twisted tensor powers are constructed. These embeddings allow for the interpretation of the canonical tensor, presenting a pairing of $\cal A$ with ${\cal A}\sp 0$ where ${\cal A}\sp 0$ is the dual Hopf algebra with opposite comultiplication, as a solution of the Yang-Baxter or Pentagon equation.
[S.Khoroshkin (Moskva)]

MSC 2000:: *17B37 Quantum groups and related deformations
16W30 Hopf algebras (assoc. rings and algebras)
46L99 Selfadjoint operator algebras
81R50 Quantum groups and related algebraic methods in quantum theory

Keywords: Yang-Baxter equation; finite-dimensional *-Hopf algebra; quantum double; Pentagon equation

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